How does the flow within the boundary layer influence morphological stability of a vicinal face?

Abstract

Imagine parallel growth steps forming a vacinal face and moving in the same direction. Since the diffusion fields of these steps overlap, the steps decelerate one another and spontaneously form macroscopic bunches. Such instability is known always to develop in supersaturated solutions and supercooled melts despite capillarity. The corresponding stability problems were analyzed previously with the assumption that the fuid within the boundary layer is stagnant. In this paper, the effect of solution flow within the boundary layer on the stability is considered for the first time. The analytical solution found describes the drift of diffusion clouds (enriched or improverished regions of solution) surrounding spontaneously appearing slight step bunches. This drift turns out to enhance instability if the fluid flow direction is the same as the step motion direction. However, if these directions are antiparallel, the drift is a very strong stabilizing factor which keeps the interface stable up to large (many cm) size. This stability is provided by the drift, in cooperation with the growth rate anisotropy. For isotropic growth kinetics, this flow-kinetic stabilization is absent. The flow-kinetic stabilization is several orders of magnitude stronger than the stabilization by capillarity. In solutions, very low flow rates, just exceeding the step growth rates, are sufficient for the stabilization. In melts, the step motion is very fast and is equivalent to the opposite fluid flow thus providing kinetic stabilization per se. The analytical solution obtained may be used in other crystal growth problems.